Answer each of the following independent questions. 1. Alex Meir recently won a lottery and has the option of receiving one of the following three prizes: (1) $64,000 cash immediately, (2) $20,000 cash immediately and a six-period annuity of $8,000 beginning one year from today, or (3) a six-period annuity of $13,000 beginning one year from today. Assuming an interest rate of 6%, which option should Alex choose?
2. The Weimer Corporation wants to accumulate a sum of money to repay certain debts due on December 31, 2025. Weimer will make annual deposits of $100,000 into a special bank account at the end of each of 10 years beginning December 31, 2016. Assuming that the bank account pays 7% interest compounded annually, what will be the fund balance after the last payment is made on December 31, 2025?

option 1

$1,381,644.80

Explanation:

Alex would choose the option that has the highest present value

Present value is the sum of discounted cash flows

Present value can be calculated using a financial calculator

pv of option 2

Cash flow in year 0 = 20,000

Cash flow in year 1 - 6 =  $8,000

i = 6%

PV = 59,338.60

OPTION 3

Cash flow in year 1 - 6 = 13,000

i - 6%

pv = 63,925.22

option 1 has the highest present value and should be chosen  

To find the PV using a financial calculator:

1. Input the cash flow values by pressing the CF button. After inputting the value, press enter and the arrow facing a downward direction.

2. after inputting all the cash flows, press the NPV button, input the value for I, press enter and the arrow facing a downward direction.  

3. Press compute  

2.

future value of an annuity = Annual payment x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

(1.07^10 - 1 ) / 0.07 = 13.816448

13.816448 x 100,000 = $1,381,644.80

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